Resol [(3/5xy)^2:(3/5x)]^3:(3/5x)^2}:(3/5y^2)

$$[ ( \frac { 3 } { 5 } x y ) ^ { 2 } : ( \frac { 3 } { 5 } x ) ] ^ { 3 } : ( \frac { 3 } { 5 } x ) ^ { 2 } \} : ( \frac { 3 } { 5 } y ^ { 2 } )$$

Calcula

$$\frac{3xy^{6}}{5}$$

Passos de solució

Expandiu \left(\frac{3}{5}xy\right)^{2}.

$$\frac{\left(\frac{\left(\frac{3}{5}\right)^{2}x^{2}y^{2}}{\frac{3}{5}x}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Calculeu \frac{3}{5} elevat a 2 per obtenir \frac{9}{25}.

$$\frac{\left(\frac{\frac{9}{25}x^{2}y^{2}}{\frac{3}{5}x}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Anul·leu x tant al numerador com al denominador.

$$\frac{\left(\frac{\frac{9}{25}xy^{2}}{\frac{3}{5}}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Dividiu \frac{9}{25}xy^{2} per \frac{3}{5} multiplicant \frac{9}{25}xy^{2} pel recíproc de \frac{3}{5}.

$$\frac{\left(\frac{\frac{9}{25}xy^{2}\times 5}{3}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Multipliqueu \frac{9}{25} per 5 per obtenir \frac{9}{5}.

$$\frac{\left(\frac{\frac{9}{5}xy^{2}}{3}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Dividiu \frac{9}{5}xy^{2} entre 3 per obtenir \frac{3}{5}xy^{2}.

$$\frac{\left(\frac{3}{5}xy^{2}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Expandiu \left(\frac{3}{5}xy^{2}\right)^{3}.

$$\frac{\left(\frac{3}{5}\right)^{3}x^{3}\left(y^{2}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Per elevar una potència a una altra potència, multipliqueu-ne els exponents. Multipliqueu 2 i 3 per obtenir 6.

$$\frac{\left(\frac{3}{5}\right)^{3}x^{3}y^{6}}{\left(\frac{3}{5}x\right)^{2}}$$

Calculeu \frac{3}{5} elevat a 3 per obtenir \frac{27}{125}.

$$\frac{\frac{27}{125}x^{3}y^{6}}{\left(\frac{3}{5}x\right)^{2}}$$

Expandiu \left(\frac{3}{5}x\right)^{2}.

$$\frac{\frac{27}{125}x^{3}y^{6}}{\left(\frac{3}{5}\right)^{2}x^{2}}$$

Calculeu \frac{3}{5} elevat a 2 per obtenir \frac{9}{25}.

$$\frac{\frac{27}{125}x^{3}y^{6}}{\frac{9}{25}x^{2}}$$

Anul·leu x^{2} tant al numerador com al denominador.

$$\frac{\frac{27}{125}xy^{6}}{\frac{9}{25}}$$

Dividiu \frac{27}{125}xy^{6} per \frac{9}{25} multiplicant \frac{27}{125}xy^{6} pel recíproc de \frac{9}{25}.

$$\frac{\frac{27}{125}xy^{6}\times 25}{9}$$

Multipliqueu \frac{27}{125} per 25 per obtenir \frac{27}{5}.

$$\frac{\frac{27}{5}xy^{6}}{9}$$

Dividiu \frac{27}{5}xy^{6} entre 9 per obtenir \frac{3}{5}xy^{6}.

$$\frac{3}{5}xy^{6}$$

Expandiu

$$\frac{3xy^{6}}{5}$$

Passos de solució

Expandiu \left(\frac{3}{5}xy\right)^{2}.

$$\frac{\left(\frac{\left(\frac{3}{5}\right)^{2}x^{2}y^{2}}{\frac{3}{5}x}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Calculeu \frac{3}{5} elevat a 2 per obtenir \frac{9}{25}.

$$\frac{\left(\frac{\frac{9}{25}x^{2}y^{2}}{\frac{3}{5}x}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Anul·leu x tant al numerador com al denominador.

$$\frac{\left(\frac{\frac{9}{25}xy^{2}}{\frac{3}{5}}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Dividiu \frac{9}{25}xy^{2} per \frac{3}{5} multiplicant \frac{9}{25}xy^{2} pel recíproc de \frac{3}{5}.

$$\frac{\left(\frac{\frac{9}{25}xy^{2}\times 5}{3}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Multipliqueu \frac{9}{25} per 5 per obtenir \frac{9}{5}.

$$\frac{\left(\frac{\frac{9}{5}xy^{2}}{3}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Dividiu \frac{9}{5}xy^{2} entre 3 per obtenir \frac{3}{5}xy^{2}.

$$\frac{\left(\frac{3}{5}xy^{2}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Expandiu \left(\frac{3}{5}xy^{2}\right)^{3}.

$$\frac{\left(\frac{3}{5}\right)^{3}x^{3}\left(y^{2}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Per elevar una potència a una altra potència, multipliqueu-ne els exponents. Multipliqueu 2 i 3 per obtenir 6.

$$\frac{\left(\frac{3}{5}\right)^{3}x^{3}y^{6}}{\left(\frac{3}{5}x\right)^{2}}$$

Calculeu \frac{3}{5} elevat a 3 per obtenir \frac{27}{125}.

$$\frac{\frac{27}{125}x^{3}y^{6}}{\left(\frac{3}{5}x\right)^{2}}$$

Expandiu \left(\frac{3}{5}x\right)^{2}.

$$\frac{\frac{27}{125}x^{3}y^{6}}{\left(\frac{3}{5}\right)^{2}x^{2}}$$

Calculeu \frac{3}{5} elevat a 2 per obtenir \frac{9}{25}.

$$\frac{\frac{27}{125}x^{3}y^{6}}{\frac{9}{25}x^{2}}$$

Anul·leu x^{2} tant al numerador com al denominador.

$$\frac{\frac{27}{125}xy^{6}}{\frac{9}{25}}$$

Dividiu \frac{27}{125}xy^{6} per \frac{9}{25} multiplicant \frac{27}{125}xy^{6} pel recíproc de \frac{9}{25}.

$$\frac{\frac{27}{125}xy^{6}\times 25}{9}$$

Multipliqueu \frac{27}{125} per 25 per obtenir \frac{27}{5}.

$$\frac{\frac{27}{5}xy^{6}}{9}$$

Dividiu \frac{27}{5}xy^{6} entre 9 per obtenir \frac{3}{5}xy^{6}.

$$\frac{3}{5}xy^{6}$$